Psychometrika

, Volume 45, Issue 1, pp 135–137 | Cite as

A new solution to the problem of finding all numerical solutions to ordered metric structures

  • Paul E. Lehner
  • Elliot Noma
Notes And Comments

Abstract

A new algorithm is used to test and describe the set of all possible solutions for any linear model of an empirical ordering derived from techniques such as additive conjoint measurement, unfolding theory, general Fechnerian scaling and ordinal multiple regression. The algorithm is computationally faster and numerically superior to previous algorithms.

Key words

ordered metric structures convex cone additive conjoint measurement unfolding theory Fechnerian scaling 

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Reference note

  1. Mattheiss, T. H. & Rubin, D. S.A survey and comparison of methods for finding all vertices of convex polyhedral sets (Tech. Rep. No. 77-14). Chapel Hill: Curriculum in Operations Research, University of North Carolina at Chapel Hill, November 1977.Google Scholar

References

  1. Chernikova, N. V. Algorithm for finding a general formula for the nonnegative solutions of a system of linear inequalities.U.S.S.R. Computational Mathematics and Mathematical Physics, 1965,5, 228–233.Google Scholar
  2. Coombs, C. H.A theory of data. New York: Wiley, 1964.Google Scholar
  3. Goode, F. M. An algorithm for the additive conjoint measurement of finite data matrices.American Psychologist, 1964,19, 579.Google Scholar
  4. McClelland, G. H. & Coombs, C. H. ORDMET, A general algorithm for constructing all numerical solutions to ordered metric structures.Psychometrika, 1975,40, 269–290.Google Scholar
  5. Motzkin, T. S., Raiffa, H., Thompson, G. L., & Thrall, R. M., The double description method. In H. W. Kuhn & A. W. Tucker (eds.),Contributions to the Theory of Games, II. Annals of Mathematics Study, No. 28, Princeton, N.J.: Princeton University Press, 1953.Google Scholar
  6. Murty, K. G.Linear and combinatorial programming. New York: Wiley, 1976.Google Scholar
  7. Phillips, J. P. N. A note on the representation of ordered metric scaling.British Journal of Mathematical and Statistical Psychology, 1971,24, 239–250.Google Scholar
  8. Wetz, R. J. B. & Witzgall, C. Algorithms for frames and linearity of cones.Journal of Research of the National Bureau of Standards, 1967,71B, 1–7.Google Scholar

Copyright information

© The Psychometric Society 1980

Authors and Affiliations

  • Paul E. Lehner
    • 1
  • Elliot Noma
    • 1
  1. 1.Department of PsychologyUniversity of MichiganAnn Arbor

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